This paper develops a neoclassical growth model to analyze the macroeconomic consequences of imperfect substitutability between native and migrant workers. We demonstrate that a permanent increase in the immigration rate raises effective labor per capita and steady-state income per capita if and only if the share of migrants in the population remains below a critical threshold. This threshold depends on the elasticity of substitution between natives and migrants and their relative productivity. Using a panel of 18 European countries from 1985 to 2022, we empirically validate our theoretical predictions through a structural panel VAR analysis. Our results show that immigration has a statistically significant positive effect on both employment and output per capita, consistent with parameter configurations in which the migrant share in our sample being below the critical threshold. These findings challenge the conventional wisdom of capital dilution effects and highlight the importance of accounting for labor market complementarities in macroeconomic analyses of immigration.